--- Stage 1 ---
Workflow: Step 1 - Equal randomization to all dose levels
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.252 0.286 0.371 0.551 0.644
Summary: Efficacy marginal means: 0.171 0.256 0.358 0.522 0.687
Summary: Immune response means: 0.158 0.239 0.531 0.604 0.684
Dose 1 : P(Tox < 0.35 ) = 0.84 (Threshold: 0.5 ) P(Eff > 0.1 ) = 0.76 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.31 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.35 ) = 0.75 (Threshold: 0.5 ) P(Eff > 0.1 ) = 0.96 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.55 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.35 ) = 0.44 (Threshold: 0.5 ) P(Eff > 0.1 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.99 (Threshold: 0.5 )
Dose 4 : P(Tox < 0.35 ) = 0.04 (Threshold: 0.5 ) P(Eff > 0.1 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 1 (Threshold: 0.5 )
Dose 5 : P(Tox < 0.35 ) = 0 (Threshold: 0.5 ) P(Eff > 0.1 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 1 (Threshold: 0.5 )
=======
This chunk runs the multi-stage trial simulation by calling the run_trial_simulation function. The simulation follows the workflow specified in TRIAL_DESIGN.md:
Stage 1 : Equal randomization to all dose levels
Interim Analysis : Update admissible set based on posterior probabilities
Adaptive Randomization : Allocate patients based on utility scores
Early Termination Check : Terminate if admissible set is empty
Final Selection : Choose OD with highest utility from admissible set + PoC validation
results <- run_trial_simulation (trial_config, p_YI, p_YT_given_I, p_YE_given_I, rho0, rho1)
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.238 0.272 0.338 0.358 0.412
Summary: Efficacy marginal means: 0.321 0.41 0.468 0.55 0.782
Summary: Immune response means: 0.159 0.24 0.479 0.517 0.81
Dose 1 : P(Tox < 0.35 ) = 0.9 (Threshold: 0.5 ) P(Eff > 0.1 ) = 0.97 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.33 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.35 ) = 0.82 (Threshold: 0.5 ) P(Eff > 0.1 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.56 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.35 ) = 0.58 (Threshold: 0.5 ) P(Eff > 0.1 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.99 (Threshold: 0.5 )
Dose 4 : P(Tox < 0.35 ) = 0.47 (Threshold: 0.5 ) P(Eff > 0.1 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.99 (Threshold: 0.5 )
Dose 5 : P(Tox < 0.35 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.1 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 1 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2 3
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.159
Toxicity given I=0 (π_T|I=0): 0.22
Toxicity given I=1 (π_T|I=1): 0.34
Efficacy given I=0 (π_E|I=0): 0.3
Efficacy given I=1 (π_E|I=1): 0.43
Probability distributions:
P(T=0|I=0): 0.78 P(T=1|I=0): 0.22
P(T=0|I=1): 0.66 P(T=1|I=1): 0.34
P(E=0|I=0): 0.7 P(E=1|I=0): 0.3
P(E=0|I=1): 0.57 P(E=1|I=1): 0.43
Expected utility given I=0: 20.69
Expected utility given I=1: 37.97
Total expected utility: 23.43
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.24
Toxicity given I=0 (π_T|I=0): 0.238
Toxicity given I=1 (π_T|I=1): 0.379
Efficacy given I=0 (π_E|I=0): 0.382
Efficacy given I=1 (π_E|I=1): 0.501
Probability distributions:
P(T=0|I=0): 0.762 P(T=1|I=0): 0.238
P(T=0|I=1): 0.621 P(T=1|I=1): 0.379
P(E=0|I=0): 0.618 P(E=1|I=0): 0.382
P(E=0|I=1): 0.499 P(E=1|I=1): 0.501
Expected utility given I=0: 26.04
Expected utility given I=1: 41.85
Total expected utility: 29.84
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.479
Toxicity given I=0 (π_T|I=0): 0.282
Toxicity given I=1 (π_T|I=1): 0.398
Efficacy given I=0 (π_E|I=0): 0.387
Efficacy given I=1 (π_E|I=1): 0.556
Probability distributions:
P(T=0|I=0): 0.718 P(T=1|I=0): 0.282
P(T=0|I=1): 0.602 P(T=1|I=1): 0.398
P(E=0|I=0): 0.613 P(E=1|I=0): 0.387
P(E=0|I=1): 0.444 P(E=1|I=1): 0.556
Expected utility given I=0: 25.51
Expected utility given I=1: 45
Total expected utility: 34.85
Dose 4 Utility Calculation:
Immune response probability (π_I): 0.517
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.404
Efficacy given I=0 (π_E|I=0): 0.403
Efficacy given I=1 (π_E|I=1): 0.689
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.596 P(T=1|I=1): 0.404
P(E=0|I=0): 0.597 P(E=1|I=0): 0.403
P(E=0|I=1): 0.311 P(E=1|I=1): 0.689
Expected utility given I=0: 26.01
Expected utility given I=1: 54.04
Total expected utility: 40.49
Dose 5 Utility Calculation:
Immune response probability (π_I): 0.81
Toxicity given I=0 (π_T|I=0): 0.377
Toxicity given I=1 (π_T|I=1): 0.42
Efficacy given I=0 (π_E|I=0): 0.56
Efficacy given I=1 (π_E|I=1): 0.835
Probability distributions:
P(T=0|I=0): 0.623 P(T=1|I=0): 0.377
P(T=0|I=1): 0.58 P(T=1|I=1): 0.42
P(E=0|I=0): 0.44 P(E=1|I=0): 0.56
P(E=0|I=1): 0.165 P(E=1|I=1): 0.835
Expected utility given I=0: 34.24
Expected utility given I=1: 63.45
Total expected utility: 57.89
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.159 | 0.220 | 0.340 | 0.300 | 0.430 | 20.7 | 38.0 | 23.4
2 | 0.240 | 0.238 | 0.379 | 0.382 | 0.501 | 26.0 | 41.8 | 29.8
3 | 0.479 | 0.282 | 0.398 | 0.387 | 0.556 | 25.5 | 45.0 | 34.8
4 | 0.517 | 0.309 | 0.404 | 0.403 | 0.689 | 26.0 | 54.0 | 40.5
5 | 0.810 | 0.377 | 0.420 | 0.560 | 0.835 | 34.2 | 63.5 | 57.9
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0 0.4612858 0.5387142 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.147 0.17 0.258 0.308 0.375
Summary: Efficacy marginal means: 0.289 0.345 0.406 0.535 0.774
Summary: Immune response means: 0.158 0.272 0.544 0.564 0.815
Dose 1 : P(Tox < 0.35 ) = 1 (Threshold: 0.5 ) P(Eff > 0.1 ) = 0.97 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.32 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.35 ) = 1 (Threshold: 0.5 ) P(Eff > 0.1 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.71 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.35 ) = 0.91 (Threshold: 0.5 ) P(Eff > 0.1 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 1 (Threshold: 0.5 )
Dose 4 : P(Tox < 0.35 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.1 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 1 (Threshold: 0.5 )
Dose 5 : P(Tox < 0.35 ) = 0.48 (Threshold: 0.5 ) P(Eff > 0.1 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 1 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2 3 4
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.158
Toxicity given I=0 (π_T|I=0): 0.126
Toxicity given I=1 (π_T|I=1): 0.258
Efficacy given I=0 (π_E|I=0): 0.278
Efficacy given I=1 (π_E|I=1): 0.35
Probability distributions:
P(T=0|I=0): 0.874 P(T=1|I=0): 0.126
P(T=0|I=1): 0.742 P(T=1|I=1): 0.258
P(E=0|I=0): 0.722 P(E=1|I=0): 0.278
P(E=0|I=1): 0.65 P(E=1|I=1): 0.35
Expected utility given I=0: 20.48
Expected utility given I=1: 34.44
Total expected utility: 22.69
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.272
Toxicity given I=0 (π_T|I=0): 0.13
Toxicity given I=1 (π_T|I=1): 0.277
Efficacy given I=0 (π_E|I=0): 0.332
Efficacy given I=1 (π_E|I=1): 0.382
Probability distributions:
P(T=0|I=0): 0.87 P(T=1|I=0): 0.13
P(T=0|I=1): 0.723 P(T=1|I=1): 0.277
P(E=0|I=0): 0.668 P(E=1|I=0): 0.332
P(E=0|I=1): 0.618 P(E=1|I=1): 0.382
Expected utility given I=0: 24.37
Expected utility given I=1: 36.3
Total expected utility: 27.62
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.544
Toxicity given I=0 (π_T|I=0): 0.179
Toxicity given I=1 (π_T|I=1): 0.323
Efficacy given I=0 (π_E|I=0): 0.333
Efficacy given I=1 (π_E|I=1): 0.467
Probability distributions:
P(T=0|I=0): 0.821 P(T=1|I=0): 0.179
P(T=0|I=1): 0.677 P(T=1|I=1): 0.323
P(E=0|I=0): 0.667 P(E=1|I=0): 0.333
P(E=0|I=1): 0.533 P(E=1|I=1): 0.467
Expected utility given I=0: 23.63
Expected utility given I=1: 41.24
Total expected utility: 33.2
Dose 4 Utility Calculation:
Immune response probability (π_I): 0.564
Toxicity given I=0 (π_T|I=0): 0.248
Toxicity given I=1 (π_T|I=1): 0.355
Efficacy given I=0 (π_E|I=0): 0.364
Efficacy given I=1 (π_E|I=1): 0.669
Probability distributions:
P(T=0|I=0): 0.752 P(T=1|I=0): 0.248
P(T=0|I=1): 0.645 P(T=1|I=1): 0.355
P(E=0|I=0): 0.636 P(E=1|I=0): 0.364
P(E=0|I=1): 0.331 P(E=1|I=1): 0.669
Expected utility given I=0: 24.6
Expected utility given I=1: 54.79
Total expected utility: 41.62
Dose 5 Utility Calculation:
Immune response probability (π_I): 0.815
Toxicity given I=0 (π_T|I=0): 0.343
Toxicity given I=1 (π_T|I=1): 0.382
Efficacy given I=0 (π_E|I=0): 0.551
Efficacy given I=1 (π_E|I=1): 0.825
Probability distributions:
P(T=0|I=0): 0.657 P(T=1|I=0): 0.343
P(T=0|I=1): 0.618 P(T=1|I=1): 0.382
P(E=0|I=0): 0.449 P(E=1|I=0): 0.551
P(E=0|I=1): 0.175 P(E=1|I=1): 0.825
Expected utility given I=0: 34.6
Expected utility given I=1: 64.65
Total expected utility: 59.09
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.158 | 0.126 | 0.258 | 0.278 | 0.350 | 20.5 | 34.4 | 22.7
2 | 0.272 | 0.130 | 0.277 | 0.332 | 0.382 | 24.4 | 36.3 | 27.6
3 | 0.544 | 0.179 | 0.323 | 0.333 | 0.467 | 23.6 | 41.2 | 33.2
4 | 0.564 | 0.248 | 0.355 | 0.364 | 0.669 | 24.6 | 54.8 | 41.6
5 | 0.815 | 0.343 | 0.382 | 0.551 | 0.825 | 34.6 | 64.6 | 59.1
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0 0.2695908 0.3241299 0.4062793 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.124 0.14 0.203 0.224 0.333
Summary: Efficacy marginal means: 0.304 0.373 0.449 0.528 0.768
Summary: Immune response means: 0.178 0.321 0.51 0.517 0.809
Dose 1 : P(Tox < 0.35 ) = 1 (Threshold: 0.5 ) P(Eff > 0.1 ) = 0.97 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.4 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.35 ) = 1 (Threshold: 0.5 ) P(Eff > 0.1 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.88 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.35 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.1 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 1 (Threshold: 0.5 )
Dose 4 : P(Tox < 0.35 ) = 0.96 (Threshold: 0.5 ) P(Eff > 0.1 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 1 (Threshold: 0.5 )
Dose 5 : P(Tox < 0.35 ) = 0.62 (Threshold: 0.5 ) P(Eff > 0.1 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 1 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2 3 4 5
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.178
Toxicity given I=0 (π_T|I=0): 0.11
Toxicity given I=1 (π_T|I=1): 0.19
Efficacy given I=0 (π_E|I=0): 0.294
Efficacy given I=1 (π_E|I=1): 0.349
Probability distributions:
P(T=0|I=0): 0.89 P(T=1|I=0): 0.11
P(T=0|I=1): 0.81 P(T=1|I=1): 0.19
P(E=0|I=0): 0.706 P(E=1|I=0): 0.294
P(E=0|I=1): 0.651 P(E=1|I=1): 0.349
Expected utility given I=0: 21.9
Expected utility given I=1: 36.14
Total expected utility: 24.43
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.321
Toxicity given I=0 (π_T|I=0): 0.112
Toxicity given I=1 (π_T|I=1): 0.202
Efficacy given I=0 (π_E|I=0): 0.371
Efficacy given I=1 (π_E|I=1): 0.379
Probability distributions:
P(T=0|I=0): 0.888 P(T=1|I=0): 0.112
P(T=0|I=1): 0.798 P(T=1|I=1): 0.202
P(E=0|I=0): 0.629 P(E=1|I=0): 0.371
P(E=0|I=1): 0.621 P(E=1|I=1): 0.379
Expected utility given I=0: 27.59
Expected utility given I=1: 38.24
Total expected utility: 31.01
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.51
Toxicity given I=0 (π_T|I=0): 0.162
Toxicity given I=1 (π_T|I=1): 0.242
Efficacy given I=0 (π_E|I=0): 0.392
Efficacy given I=1 (π_E|I=1): 0.503
Probability distributions:
P(T=0|I=0): 0.838 P(T=1|I=0): 0.162
P(T=0|I=1): 0.758 P(T=1|I=1): 0.242
P(E=0|I=0): 0.608 P(E=1|I=0): 0.392
P(E=0|I=1): 0.497 P(E=1|I=1): 0.503
Expected utility given I=0: 28.15
Expected utility given I=1: 46.75
Total expected utility: 37.64
Dose 4 Utility Calculation:
Immune response probability (π_I): 0.517
Toxicity given I=0 (π_T|I=0): 0.178
Toxicity given I=1 (π_T|I=1): 0.266
Efficacy given I=0 (π_E|I=0): 0.427
Efficacy given I=1 (π_E|I=1): 0.623
Probability distributions:
P(T=0|I=0): 0.822 P(T=1|I=0): 0.178
P(T=0|I=1): 0.734 P(T=1|I=1): 0.266
P(E=0|I=0): 0.573 P(E=1|I=0): 0.427
P(E=0|I=1): 0.377 P(E=1|I=1): 0.623
Expected utility given I=0: 30.33
Expected utility given I=1: 55.14
Total expected utility: 43.15
Dose 5 Utility Calculation:
Immune response probability (π_I): 0.809
Toxicity given I=0 (π_T|I=0): 0.302
Toxicity given I=1 (π_T|I=1): 0.339
Efficacy given I=0 (π_E|I=0): 0.564
Efficacy given I=1 (π_E|I=1): 0.818
Probability distributions:
P(T=0|I=0): 0.698 P(T=1|I=0): 0.302
P(T=0|I=1): 0.661 P(T=1|I=1): 0.339
P(E=0|I=0): 0.436 P(E=1|I=0): 0.564
P(E=0|I=1): 0.182 P(E=1|I=1): 0.818
Expected utility given I=0: 36.63
Expected utility given I=1: 66.34
Total expected utility: 60.66
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.178 | 0.110 | 0.190 | 0.294 | 0.349 | 21.9 | 36.1 | 24.4
2 | 0.321 | 0.112 | 0.202 | 0.371 | 0.379 | 27.6 | 38.2 | 31.0
3 | 0.510 | 0.162 | 0.242 | 0.392 | 0.503 | 28.2 | 46.8 | 37.6
4 | 0.517 | 0.178 | 0.266 | 0.427 | 0.623 | 30.3 | 55.1 | 43.1
5 | 0.809 | 0.302 | 0.339 | 0.564 | 0.818 | 36.6 | 66.3 | 60.7
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0 0.1798065 0.2182409 0.2501857 0.3517669
--- Stage 4 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.105 0.119 0.178 0.189 0.235
Summary: Efficacy marginal means: 0.286 0.337 0.471 0.534 0.801
Summary: Immune response means: 0.177 0.324 0.525 0.526 0.799
Dose 1 : P(Tox < 0.35 ) = 1 (Threshold: 0.5 ) P(Eff > 0.1 ) = 0.97 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.41 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.35 ) = 1 (Threshold: 0.5 ) P(Eff > 0.1 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.89 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.35 ) = 1 (Threshold: 0.5 ) P(Eff > 0.1 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 1 (Threshold: 0.5 )
Dose 4 : P(Tox < 0.35 ) = 1 (Threshold: 0.5 ) P(Eff > 0.1 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 1 (Threshold: 0.5 )
Dose 5 : P(Tox < 0.35 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.1 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 1 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2 3 4 5
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.177
Toxicity given I=0 (π_T|I=0): 0.092
Toxicity given I=1 (π_T|I=1): 0.166
Efficacy given I=0 (π_E|I=0): 0.278
Efficacy given I=1 (π_E|I=1): 0.325
Probability distributions:
P(T=0|I=0): 0.908 P(T=1|I=0): 0.092
P(T=0|I=1): 0.834 P(T=1|I=1): 0.166
P(E=0|I=0): 0.722 P(E=1|I=0): 0.278
P(E=0|I=1): 0.675 P(E=1|I=1): 0.325
Expected utility given I=0: 20.93
Expected utility given I=1: 34.9
Total expected utility: 23.4
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.324
Toxicity given I=0 (π_T|I=0): 0.093
Toxicity given I=1 (π_T|I=1): 0.175
Efficacy given I=0 (π_E|I=0): 0.335
Efficacy given I=1 (π_E|I=1): 0.343
Probability distributions:
P(T=0|I=0): 0.907 P(T=1|I=0): 0.093
P(T=0|I=1): 0.825 P(T=1|I=1): 0.175
P(E=0|I=0): 0.665 P(E=1|I=0): 0.335
P(E=0|I=1): 0.657 P(E=1|I=1): 0.343
Expected utility given I=0: 25.21
Expected utility given I=1: 36.16
Total expected utility: 28.76
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.525
Toxicity given I=0 (π_T|I=0): 0.131
Toxicity given I=1 (π_T|I=1): 0.221
Efficacy given I=0 (π_E|I=0): 0.349
Efficacy given I=1 (π_E|I=1): 0.581
Probability distributions:
P(T=0|I=0): 0.869 P(T=1|I=0): 0.131
P(T=0|I=1): 0.779 P(T=1|I=1): 0.221
P(E=0|I=0): 0.651 P(E=1|I=0): 0.349
P(E=0|I=1): 0.419 P(E=1|I=1): 0.581
Expected utility given I=0: 25.67
Expected utility given I=1: 53.67
Total expected utility: 40.36
Dose 4 Utility Calculation:
Immune response probability (π_I): 0.526
Toxicity given I=0 (π_T|I=0): 0.139
Toxicity given I=1 (π_T|I=1): 0.235
Efficacy given I=0 (π_E|I=0): 0.359
Efficacy given I=1 (π_E|I=1): 0.691
Probability distributions:
P(T=0|I=0): 0.861 P(T=1|I=0): 0.139
P(T=0|I=1): 0.765 P(T=1|I=1): 0.235
P(E=0|I=0): 0.641 P(E=1|I=0): 0.359
P(E=0|I=1): 0.309 P(E=1|I=1): 0.691
Expected utility given I=0: 26.23
Expected utility given I=1: 61.74
Total expected utility: 44.9
Dose 5 Utility Calculation:
Immune response probability (π_I): 0.799
Toxicity given I=0 (π_T|I=0): 0.205
Toxicity given I=1 (π_T|I=1): 0.242
Efficacy given I=0 (π_E|I=0): 0.442
Efficacy given I=1 (π_E|I=1): 0.891
Probability distributions:
P(T=0|I=0): 0.795 P(T=1|I=0): 0.205
P(T=0|I=1): 0.758 P(T=1|I=1): 0.242
P(E=0|I=0): 0.558 P(E=1|I=0): 0.442
P(E=0|I=1): 0.109 P(E=1|I=1): 0.891
Expected utility given I=0: 30.8
Expected utility given I=1: 76.98
Total expected utility: 67.69
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.177 | 0.092 | 0.166 | 0.278 | 0.325 | 20.9 | 34.9 | 23.4
2 | 0.324 | 0.093 | 0.175 | 0.335 | 0.343 | 25.2 | 36.2 | 28.8
3 | 0.525 | 0.131 | 0.221 | 0.349 | 0.581 | 25.7 | 53.7 | 40.4
4 | 0.526 | 0.139 | 0.235 | 0.359 | 0.691 | 26.2 | 61.7 | 44.9
5 | 0.799 | 0.205 | 0.242 | 0.442 | 0.891 | 30.8 | 77.0 | 67.7
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0 0.1582726 0.2221118 0.2471072 0.3725084
--- Stage 5 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.092 0.107 0.163 0.177 0.219
Summary: Efficacy marginal means: 0.277 0.319 0.491 0.556 0.745
Summary: Immune response means: 0.173 0.343 0.533 0.534 0.641
Dose 1 : P(Tox < 0.35 ) = 1 (Threshold: 0.5 ) P(Eff > 0.1 ) = 0.97 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.39 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.35 ) = 1 (Threshold: 0.5 ) P(Eff > 0.1 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.94 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.35 ) = 1 (Threshold: 0.5 ) P(Eff > 0.1 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 1 (Threshold: 0.5 )
Dose 4 : P(Tox < 0.35 ) = 1 (Threshold: 0.5 ) P(Eff > 0.1 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 1 (Threshold: 0.5 )
Dose 5 : P(Tox < 0.35 ) = 0.96 (Threshold: 0.5 ) P(Eff > 0.1 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 1 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2 3 4 5
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.173
Toxicity given I=0 (π_T|I=0): 0.08
Toxicity given I=1 (π_T|I=1): 0.15
Efficacy given I=0 (π_E|I=0): 0.27
Efficacy given I=1 (π_E|I=1): 0.306
Probability distributions:
P(T=0|I=0): 0.92 P(T=1|I=0): 0.08
P(T=0|I=1): 0.85 P(T=1|I=1): 0.15
P(E=0|I=0): 0.73 P(E=1|I=0): 0.27
P(E=0|I=1): 0.694 P(E=1|I=1): 0.306
Expected utility given I=0: 20.51
Expected utility given I=1: 33.78
Total expected utility: 22.8
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.343
Toxicity given I=0 (π_T|I=0): 0.081
Toxicity given I=1 (π_T|I=1): 0.157
Efficacy given I=0 (π_E|I=0): 0.318
Efficacy given I=1 (π_E|I=1): 0.322
Probability distributions:
P(T=0|I=0): 0.919 P(T=1|I=0): 0.081
P(T=0|I=1): 0.843 P(T=1|I=1): 0.157
P(E=0|I=0): 0.682 P(E=1|I=0): 0.318
P(E=0|I=1): 0.678 P(E=1|I=1): 0.322
Expected utility given I=0: 24.15
Expected utility given I=1: 34.88
Total expected utility: 27.83
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.533
Toxicity given I=0 (π_T|I=0): 0.114
Toxicity given I=1 (π_T|I=1): 0.205
Efficacy given I=0 (π_E|I=0): 0.327
Efficacy given I=1 (π_E|I=1): 0.634
Probability distributions:
P(T=0|I=0): 0.886 P(T=1|I=0): 0.114
P(T=0|I=1): 0.795 P(T=1|I=1): 0.205
P(E=0|I=0): 0.673 P(E=1|I=0): 0.327
P(E=0|I=1): 0.366 P(E=1|I=1): 0.634
Expected utility given I=0: 24.33
Expected utility given I=1: 58.52
Total expected utility: 42.55
Dose 4 Utility Calculation:
Immune response probability (π_I): 0.534
Toxicity given I=0 (π_T|I=0): 0.119
Toxicity given I=1 (π_T|I=1): 0.228
Efficacy given I=0 (π_E|I=0): 0.336
Efficacy given I=1 (π_E|I=1): 0.747
Probability distributions:
P(T=0|I=0): 0.881 P(T=1|I=0): 0.119
P(T=0|I=1): 0.772 P(T=1|I=1): 0.228
P(E=0|I=0): 0.664 P(E=1|I=0): 0.336
P(E=0|I=1): 0.253 P(E=1|I=1): 0.747
Expected utility given I=0: 24.89
Expected utility given I=1: 66.41
Total expected utility: 47.06
Dose 5 Utility Calculation:
Immune response probability (π_I): 0.641
Toxicity given I=0 (π_T|I=0): 0.201
Toxicity given I=1 (π_T|I=1): 0.229
Efficacy given I=0 (π_E|I=0): 0.576
Efficacy given I=1 (π_E|I=1): 0.84
Probability distributions:
P(T=0|I=0): 0.799 P(T=1|I=0): 0.201
P(T=0|I=1): 0.771 P(T=1|I=1): 0.229
P(E=0|I=0): 0.424 P(E=1|I=0): 0.576
P(E=0|I=1): 0.16 P(E=1|I=1): 0.84
Expected utility given I=0: 40.29
Expected utility given I=1: 73.67
Total expected utility: 61.69
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.173 | 0.080 | 0.150 | 0.270 | 0.306 | 20.5 | 33.8 | 22.8
2 | 0.343 | 0.081 | 0.157 | 0.318 | 0.322 | 24.2 | 34.9 | 27.8
3 | 0.533 | 0.114 | 0.205 | 0.327 | 0.634 | 24.3 | 58.5 | 42.5
4 | 0.534 | 0.119 | 0.228 | 0.336 | 0.747 | 24.9 | 66.4 | 47.1
5 | 0.641 | 0.201 | 0.229 | 0.576 | 0.840 | 40.3 | 73.7 | 61.7
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.440±0.103, Πᵢⱼ=0.732±0.101, PoC=0.854
PoC calculation for dose 3: Πᵢ=0.503±0.091, Πᵢⱼ=0.732±0.101, PoC=0.759
PoC calculation for dose 4: Πᵢ=0.508±0.101, Πᵢⱼ=0.732±0.101, PoC=0.724
PoC calculation for dose 5: Πᵢ=0.732±0.101, Πᵢⱼ=0.732±0.101, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0.854
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2 3 4 5
Utilities: 27.83 42.55 47.06 61.69
Selected dose: 5
Selected utility: 61.69
PoC validated: FALSE
Max PoC probability: 0.854
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
Results
This chunk prints the final optimal dose and displays the plots.
# Print final results
cat ("
--- Final Results ---
" )
if (results$ terminated_early) {
cat ("Trial terminated early at stage:" , results$ termination_stage, "
" )
cat ("Reason:" , results$ termination_reason, "
" )
cat ("No Optimal Dose selected
" )
} else {
cat ("Final OD:" , results$ final_od, "
" )
cat ("Final utility:" , round (results$ final_utility, 2 ), "
" )
cat ("PoC validated:" , results$ poc_validated, "
" )
cat ("PoC probability:" , round (results$ poc_probability, 3 ), "
" )
cat ("Selection reason:" , results$ selection_reason, "
" )
}
Final OD: 5
Final utility: 61.69
PoC validated: FALSE
PoC probability: 0.854
Selection reason: PoC threshold not met, but selecting best available dose
# Plot final results and save them with modern styling
plot_posterior_summary (results$ posterior_summaries$ imm, title = "Immune Response vs Dose (PAVA Adjusted)" , file_path = "results/plots/immune_response_refactored.png" , style = "modern" )
plot_posterior_summary (results$ posterior_summaries$ tox, title = "Toxicity Rate by Dose and Immune Status" , group_col = "Y_I" , file_path = "results/plots/toxicity_refactored.png" , style = "modern" )
plot_posterior_summary (results$ posterior_summaries$ eff, title = "Efficacy Rate by Dose and Immune Status" , group_col = "Y_I" , file_path = "results/plots/efficacy_refactored.png" , style = "modern" )
# Create dose-response curves similar to reference code
cat (" \n === Creating Dose-Response Curves === \n " )
=== Creating Dose-Response Curves ===
# Extract true probabilities for dose-response curves
true_toxicity <- p_YT_given_I[,1 ] * (1 - p_YI) + p_YT_given_I[,2 ] * p_YI
true_efficacy <- p_YE_given_I[,1 ] * (1 - p_YI) + p_YE_given_I[,2 ] * p_YI
true_utility <- results$ final_utility_by_dose
# Create dose-response curves plot
dose_response_plot <- plot_dose_response_curves (
toxicity_data = true_toxicity,
efficacy_data = true_efficacy,
utility_data = true_utility,
title = "True Dose-Response Curves" ,
file_path = "results/plots/dose_response_curves.png"
)
Warning: Removed 3 rows containing missing values or values outside the scale range
(`geom_line()`).
Warning: Removed 3 rows containing missing values or values outside the scale range
(`geom_point()`).
print (dose_response_plot)
Warning: Removed 3 rows containing missing values or values outside the scale range
(`geom_line()`).
Removed 3 rows containing missing values or values outside the scale range
(`geom_point()`).
# Plot allocation probabilities over time with modern styling
p_alloc_time <- ggplot (results$ all_alloc_probs, aes (x = Stage, y = Prob, color = factor (Dose))) +
geom_line (linewidth = 1 ) +
geom_point (size = 3 ) +
labs (title = "Allocation Probabilities Over Time" ,
x = "Stage" , y = "Allocation Probability" ,
color = "Dose Level" ) +
scale_color_manual (values = c ("#999999" , "#E69F00" , "#56B4E9" , "#009E73" , "#CC79A7" )) +
theme_bw (base_size = 16 ) +
theme (panel.grid = element_blank (),
plot.title = element_text (hjust = 0.5 ),
axis.line = element_line (color = "black" ))
print (p_alloc_time)
# Visualize participant allocation with better formatting
# Count participants per dose level and stage
allocation_summary <- results$ all_data %>%
group_by (d, stage) %>%
summarise (n_participants = n (), .groups = 'drop' ) %>%
mutate (d = factor (d), stage = factor (stage, levels = 1 : 5 , labels = paste ("Stage" , 1 : 5 )))
# Plot 1: Allocation by dose level and stage with modern styling
p_alloc <- ggplot (allocation_summary, aes (x = d, y = n_participants, fill = stage)) +
geom_bar (stat = "identity" , position = "dodge" , width = 0.7 , color = "black" ) +
labs (title = "Participant Allocation by Dose Level and Stage" ,
x = "Dose Level" , y = "Number of Participants" ,
subtitle = paste ("Total participants:" , sum (allocation_summary$ n_participants))) +
scale_fill_manual (name = "Stage" , values = c ("#999999" , "#E69F00" , "#56B4E9" , "#009E73" , "#CC79A7" )) +
theme_bw (base_size = 16 ) +
theme (panel.grid = element_blank (),
plot.title = element_text (size = 14 , face = "bold" , hjust = 0.5 ),
axis.text = element_text (size = 12 ),
axis.title = element_text (size = 12 ),
axis.line = element_line (color = "black" ))
print (p_alloc)
# Plot 2: Cumulative allocation over stages
cumulative_summary <- allocation_summary %>%
group_by (d) %>%
mutate (cumulative_participants = cumsum (n_participants)) %>%
ungroup ()
p_cumulative <- ggplot (cumulative_summary, aes (x = stage, y = cumulative_participants, color = d, group = d)) +
geom_line (linewidth = 1.5 ) +
geom_point (size = 3 ) +
labs (title = "Cumulative Participant Allocation Over Stages" ,
x = "Stage" , y = "Cumulative Number of Participants" ,
color = "Dose Level" ,
subtitle = paste ("Final total participants:" , sum (allocation_summary$ n_participants))) +
scale_color_manual (values = c ("#999999" , "#E69F00" , "#56B4E9" , "#009E73" , "#CC79A7" )) +
theme_bw (base_size = 16 ) +
theme (panel.grid = element_blank (),
plot.title = element_text (size = 14 , face = "bold" , hjust = 0.5 ),
axis.text = element_text (size = 12 ),
axis.title = element_text (size = 12 ),
axis.line = element_line (color = "black" ))
print (p_cumulative)
# Print summary statistics
cat (" \n === ALLOCATION SUMMARY === \n " )
=== ALLOCATION SUMMARY ===
cat ("Total participants:" , sum (allocation_summary$ n_participants), " \n " )
cat ("Participants per stage: \n " )
stage_totals <- allocation_summary %>%
group_by (stage) %>%
summarise (total = sum (n_participants), .groups = 'drop' )
for (i in 1 : nrow (stage_totals)) {
cat (" Stage" , i, ":" , stage_totals$ total[i], "participants \n " )
}
Stage 1 : 15 participants
Stage 2 : 15 participants
Stage 3 : 15 participants
Stage 4 : 15 participants
Stage 5 : 15 participants
Method Comparison Analysis
This section creates comparison plots similar to the reference code, showing how different methods or parameter settings would perform.
# Create example data for method comparison (similar to reference code)
cat (" \n === Creating Method Comparison Plots === \n " )
=== Creating Method Comparison Plots ===
# Simulate different method performances
methods <- c ("Current" , "Proposed" , "Reference" )
scenarios <- c ("Scenario 1" , "Scenario 2" , "Scenario 3" )
# OBD Selection Rate Comparison
obd_data <- expand.grid (
scenario = scenarios,
method = methods,
stringsAsFactors = FALSE
)
obd_data$ obd_rate <- c (45 , 60 , 55 , 70 , 65 , 50 , 80 , 85 , 75 )
# Create OBD selection plot
p_obd <- plot_method_comparison_bars (
obd_data,
x_var = "scenario" , y_var = "obd_rate" , fill_var = "method" ,
title = "OBD Selection Rate Comparison" ,
y_label = "OBD Selection (%)" ,
limits = c (0 , 100 ),
file_path = "results/plots/obd_selection_comparison.png"
)
Warning: `aes_string()` was deprecated in ggplot2 3.0.0.
ℹ Please use tidy evaluation idioms with `aes()`.
ℹ See also `vignette("ggplot2-in-packages")` for more information.
# Sample Size Comparison
sample_data <- expand.grid (
scenario = scenarios,
method = methods,
stringsAsFactors = FALSE
)
sample_data$ avg_n <- c (25 , 20 , 30 , 22 , 18 , 28 , 18 , 15 , 25 )
# Create sample size plot
p_sample <- plot_method_comparison_bars (
sample_data,
x_var = "scenario" , y_var = "avg_n" , fill_var = "method" ,
title = "Average Sample Size Comparison" ,
y_label = "Average Sample Size" ,
limits = c (0 , 35 ),
file_path = "results/plots/sample_size_comparison.png"
)
print (p_sample)
# Safety (Overdose) Comparison
safety_data <- expand.grid (
scenario = scenarios,
method = methods,
stringsAsFactors = FALSE
)
safety_data$ overdose_pct <- c (15 , 10 , 20 , 12 , 8 , 18 , 8 , 5 , 15 )
# Create safety plot
p_safety <- plot_method_comparison_bars (
safety_data,
x_var = "scenario" , y_var = "overdose_pct" , fill_var = "method" ,
title = "Overdose Patient Percentage" ,
y_label = "Overdose Pts (%)" ,
limits = c (0 , 25 ),
file_path = "results/plots/safety_comparison.png"
)
print (p_safety)
cat ("✅ Method comparison plots created successfully! \n " )
✅ Method comparison plots created successfully!
cat ("📁 All plots saved to results/plots/ directory \n " )
📁 All plots saved to results/plots/ directory
Multi-Scenario Analysis
This section creates multi-scenario dose-response curves similar to the reference code.
# Create multi-scenario analysis
cat (" \n === Creating Multi-Scenario Analysis === \n " )
=== Creating Multi-Scenario Analysis ===
# Define different scenarios with varying parameters
scenarios_data <- list (
list (
toxicity = c (0.1 , 0.18 , 0.35 , 0.40 , 0.50 ),
efficacy = c (0.35 , 0.35 , 0.37 , 0.39 , 0.39 ),
utility = c (0.27 , 0.23 , 0.10 , 0.13 , 0.17 )
),
list (
toxicity = c (0.05 , 0.15 , 0.25 , 0.35 , 0.50 ),
efficacy = c (0.10 , 0.35 , 0.35 , 0.38 , 0.39 ),
utility = c (0.07 , 0.22 , 0.22 , 0.12 , 0.06 )
),
list (
toxicity = c (0.02 , 0.06 , 0.10 , 0.20 , 0.35 ),
efficacy = c (0.05 , 0.10 , 0.35 , 0.35 , 0.40 ),
utility = c (0.03 , 0.07 , 0.28 , 0.22 , 0.13 )
)
)
# Create multi-scenario plot
multi_scenario_plot <- plot_multi_scenario_curves (
scenarios_data,
title = "Dose-Response Curves Across Scenarios" ,
file_path = "results/plots/multi_scenario_analysis.png"
)
Scale for y is already present.
Adding another scale for y, which will replace the existing scale.
print (multi_scenario_plot)
cat ("✅ Multi-scenario analysis completed! \n " )
✅ Multi-scenario analysis completed!
Calibration Framework
This section demonstrates the calibration framework for optimizing trial parameters.
Setup Calibration
# Use absolute paths for calibration functions
project_root <- "/Users/jz/Development/DoseFinding"
# Source calibration functions
source (file.path (project_root, "src/optimization/poc_calibration.R" ))
source (file.path (project_root, "src/optimization/early_termination_calibration.R" ))
source (file.path (project_root, "src/utils/calibration_plots.R" ))
# Set up output directory for calibration results
calibration_output_dir <- "results/notebook_calibration"
dir.create (calibration_output_dir, showWarnings = FALSE , recursive = TRUE )
PoC Calibration
Calibrate the PoC threshold to achieve target detection rates in null scenarios.
# Run PoC calibration with reduced simulations for notebook
cat ("Running PoC calibration... \n " )
Running PoC calibration...
poc_results <- run_quick_calibration (
target_rate = 0.10 ,
n_simulations = 100 # Reduced for notebook
)
Running quick calibration (reduced simulations for testing)...
Starting PoC calibration...
Target detection rate: 0.1
Number of simulations per C_poc: 100
C_poc range: 0.7 to 0.95
Progress: 1/6 - Testing C_poc = 0.700
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
>>>>>>> origin/main
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
<<<<<<< HEAD
Immune response probability (π_I): 0.158
Toxicity given I=0 (π_T|I=0): 0.233
Toxicity given I=1 (π_T|I=1): 0.356
Efficacy given I=0 (π_E|I=0): 0.141
Efficacy given I=1 (π_E|I=1): 0.332
Probability distributions:
P(T=0|I=0): 0.767 P(T=1|I=0): 0.233
P(T=0|I=1): 0.644 P(T=1|I=1): 0.356
P(E=0|I=0): 0.859 P(E=1|I=0): 0.141
P(E=0|I=1): 0.668 P(E=1|I=1): 0.332
Expected utility given I=0: 9.61
Expected utility given I=1: 30.43
Total expected utility: 12.89
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.239
Toxicity given I=0 (π_T|I=0): 0.252
Toxicity given I=1 (π_T|I=1): 0.393
Efficacy given I=0 (π_E|I=0): 0.214
Efficacy given I=1 (π_E|I=1): 0.387
Probability distributions:
P(T=0|I=0): 0.748 P(T=1|I=0): 0.252
P(T=0|I=1): 0.607 P(T=1|I=1): 0.393
P(E=0|I=0): 0.786 P(E=1|I=0): 0.214
P(E=0|I=1): 0.613 P(E=1|I=1): 0.387
Expected utility given I=0: 14.41
Expected utility given I=1: 33.29
Total expected utility: 18.93
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.531
Toxicity given I=0 (π_T|I=0): 0.326
Toxicity given I=1 (π_T|I=1): 0.411
Efficacy given I=0 (π_E|I=0): 0.302
Efficacy given I=1 (π_E|I=1): 0.405
Probability distributions:
P(T=0|I=0): 0.674 P(T=1|I=0): 0.326
P(T=0|I=1): 0.589 P(T=1|I=1): 0.411
P(E=0|I=0): 0.698 P(E=1|I=0): 0.302
P(E=0|I=1): 0.595 P(E=1|I=1): 0.405
Expected utility given I=0: 19.25
Expected utility given I=1: 34.05
Total expected utility: 27.11
Dose 4 Utility Calculation:
Immune response probability (π_I): 0.604
Toxicity given I=0 (π_T|I=0): 0.52
Toxicity given I=1 (π_T|I=1): 0.571
Efficacy given I=0 (π_E|I=0): 0.46
Efficacy given I=1 (π_E|I=1): 0.562
Probability distributions:
P(T=0|I=0): 0.48 P(T=1|I=0): 0.52
P(T=0|I=1): 0.429 P(T=1|I=1): 0.571
P(E=0|I=0): 0.54 P(E=1|I=0): 0.46
P(E=0|I=1): 0.438 P(E=1|I=1): 0.562
Expected utility given I=0: 24.83
Expected utility given I=1: 38.8
Total expected utility: 33.28
Dose 5 Utility Calculation:
Immune response probability (π_I): 0.684
Toxicity given I=0 (π_T|I=0): 0.611
Toxicity given I=1 (π_T|I=1): 0.659
Efficacy given I=0 (π_E|I=0): 0.492
Efficacy given I=1 (π_E|I=1): 0.778
Probability distributions:
P(T=0|I=0): 0.389 P(T=1|I=0): 0.611
P(T=0|I=1): 0.341 P(T=1|I=1): 0.659
P(E=0|I=0): 0.508 P(E=1|I=0): 0.492
P(E=0|I=1): 0.222 P(E=1|I=1): 0.778
Expected utility given I=0: 24.33
Expected utility given I=1: 47.78
Total expected utility: 40.37
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.158 | 0.233 | 0.356 | 0.141 | 0.332 | 9.6 | 30.4 | 12.9
2 | 0.239 | 0.252 | 0.393 | 0.214 | 0.387 | 14.4 | 33.3 | 18.9
3 | 0.531 | 0.326 | 0.411 | 0.302 | 0.405 | 19.3 | 34.1 | 27.1
4 | 0.604 | 0.520 | 0.571 | 0.460 | 0.562 | 24.8 | 38.8 | 33.3
5 | 0.684 | 0.611 | 0.659 | 0.492 | 0.778 | 24.3 | 47.8 | 40.4
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0 1 0 0 0
--- Stage 2 ---
Workflow: Step 1 - Adaptive randomization (using probabilities from previous stage)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.104 0.12 0.302 0.543 0.639
Summary: Efficacy marginal means: 0.121 0.158 0.3 0.516 0.68
Summary: Immune response means: 0.144 0.216 0.526 0.6 0.68
Dose 1 : P(Tox < 0.35 ) = 1 (Threshold: 0.5 ) P(Eff > 0.1 ) = 0.59 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.27 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.35 ) = 1 (Threshold: 0.5 ) P(Eff > 0.1 ) = 0.82 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.35 ) = 0.67 (Threshold: 0.5 ) P(Eff > 0.1 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.98 (Threshold: 0.5 )
Dose 4 : P(Tox < 0.35 ) = 0.07 (Threshold: 0.5 ) P(Eff > 0.1 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 1 (Threshold: 0.5 )
Dose 5 : P(Tox < 0.35 ) = 0.01 (Threshold: 0.5 ) P(Eff > 0.1 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 1 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2 3
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.144
Toxicity given I=0 (π_T|I=0): 0.082
Toxicity given I=1 (π_T|I=1): 0.233
Efficacy given I=0 (π_E|I=0): 0.102
Efficacy given I=1 (π_E|I=1): 0.233
Probability distributions:
P(T=0|I=0): 0.918 P(T=1|I=0): 0.082
P(T=0|I=1): 0.767 P(T=1|I=1): 0.233
P(E=0|I=0): 0.898 P(E=1|I=0): 0.102
P(E=0|I=1): 0.767 P(E=1|I=1): 0.233
Expected utility given I=0: 7.71
Expected utility given I=1: 25.93
Total expected utility: 10.33
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.216
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.256
Efficacy given I=0 (π_E|I=0): 0.132
Efficacy given I=1 (π_E|I=1): 0.255
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.744 P(T=1|I=1): 0.256
P(E=0|I=0): 0.868 P(E=1|I=0): 0.132
P(E=0|I=1): 0.745 P(E=1|I=1): 0.255
Expected utility given I=0: 9.99
Expected utility given I=1: 27.15
Total expected utility: 13.7
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.526
Toxicity given I=0 (π_T|I=0): 0.251
Toxicity given I=1 (π_T|I=1): 0.348
Efficacy given I=0 (π_E|I=0): 0.257
Efficacy given I=1 (π_E|I=1): 0.34
Probability distributions:
P(T=0|I=0): 0.749 P(T=1|I=0): 0.251
P(T=0|I=1): 0.652 P(T=1|I=1): 0.348
P(E=0|I=0): 0.743 P(E=1|I=0): 0.257
P(E=0|I=1): 0.66 P(E=1|I=1): 0.34
Expected utility given I=0: 17.32
Expected utility given I=1: 31.2
Total expected utility: 24.62
Dose 4 Utility Calculation:
Immune response probability (π_I): 0.6
Toxicity given I=0 (π_T|I=0): 0.509
Toxicity given I=1 (π_T|I=1): 0.566
Efficacy given I=0 (π_E|I=0): 0.451
Efficacy given I=1 (π_E|I=1): 0.557
Probability distributions:
P(T=0|I=0): 0.491 P(T=1|I=0): 0.509
P(T=0|I=1): 0.434 P(T=1|I=1): 0.566
P(E=0|I=0): 0.549 P(E=1|I=0): 0.451
P(E=0|I=1): 0.443 P(E=1|I=1): 0.557
Expected utility given I=0: 24.6
Expected utility given I=1: 38.74
Total expected utility: 33.09
Dose 5 Utility Calculation:
Immune response probability (π_I): 0.68
Toxicity given I=0 (π_T|I=0): 0.607
Toxicity given I=1 (π_T|I=1): 0.654
Efficacy given I=0 (π_E|I=0): 0.491
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.393 P(T=1|I=0): 0.607
P(T=0|I=1): 0.346 P(T=1|I=1): 0.654
P(E=0|I=0): 0.509 P(E=1|I=0): 0.491
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 24.38
Expected utility given I=1: 47.46
Total expected utility: 40.07
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.144 | 0.082 | 0.233 | 0.102 | 0.233 | 7.7 | 25.9 | 10.3
2 | 0.216 | 0.083 | 0.256 | 0.132 | 0.255 | 10.0 | 27.2 | 13.7
3 | 0.526 | 0.251 | 0.348 | 0.257 | 0.340 | 17.3 | 31.2 | 24.6
4 | 0.600 | 0.509 | 0.566 | 0.451 | 0.557 | 24.6 | 38.7 | 33.1
5 | 0.680 | 0.607 | 0.654 | 0.491 | 0.768 | 24.4 | 47.5 | 40.1
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0 0.3575546 0.6424454 0 0
--- Stage 3 ---
Workflow: Step 1 - Adaptive randomization (using probabilities from previous stage)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.082 0.097 0.242 0.531 0.638
Summary: Efficacy marginal means: 0.153 0.212 0.441 0.544 0.697
Summary: Immune response means: 0.17 0.295 0.557 0.618 0.683
Dose 1 : P(Tox < 0.35 ) = 1 (Threshold: 0.5 ) P(Eff > 0.1 ) = 0.74 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.4 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.35 ) = 1 (Threshold: 0.5 ) P(Eff > 0.1 ) = 0.97 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.88 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.35 ) = 0.88 (Threshold: 0.5 ) P(Eff > 0.1 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 1 (Threshold: 0.5 )
Dose 4 : P(Tox < 0.35 ) = 0.08 (Threshold: 0.5 ) P(Eff > 0.1 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 1 (Threshold: 0.5 )
Dose 5 : P(Tox < 0.35 ) = 0.01 (Threshold: 0.5 ) P(Eff > 0.1 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 1 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2 3
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.17
Toxicity given I=0 (π_T|I=0): 0.067
Toxicity given I=1 (π_T|I=1): 0.155
Efficacy given I=0 (π_E|I=0): 0.127
Efficacy given I=1 (π_E|I=1): 0.277
Probability distributions:
P(T=0|I=0): 0.933 P(T=1|I=0): 0.067
P(T=0|I=1): 0.845 P(T=1|I=1): 0.155
P(E=0|I=0): 0.873 P(E=1|I=0): 0.127
P(E=0|I=1): 0.723 P(E=1|I=1): 0.277
Expected utility given I=0: 9.71
Expected utility given I=1: 31.24
Total expected utility: 13.38
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.295
Toxicity given I=0 (π_T|I=0): 0.068
Toxicity given I=1 (π_T|I=1): 0.165
Efficacy given I=0 (π_E|I=0): 0.171
Efficacy given I=1 (π_E|I=1): 0.311
Probability distributions:
P(T=0|I=0): 0.932 P(T=1|I=0): 0.068
P(T=0|I=1): 0.835 P(T=1|I=1): 0.165
P(E=0|I=0): 0.829 P(E=1|I=0): 0.171
P(E=0|I=1): 0.689 P(E=1|I=1): 0.311
Expected utility given I=0: 13.07
Expected utility given I=1: 33.79
Total expected utility: 19.18
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.557
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.259
Efficacy given I=0 (π_E|I=0): 0.374
Efficacy given I=1 (π_E|I=1): 0.494
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.741 P(T=1|I=1): 0.259
P(E=0|I=0): 0.626 P(E=1|I=0): 0.374
P(E=0|I=1): 0.506 P(E=1|I=1): 0.494
Expected utility given I=0: 25.82
Expected utility given I=1: 45.46
Total expected utility: 36.77
Dose 4 Utility Calculation:
Immune response probability (π_I): 0.618
Toxicity given I=0 (π_T|I=0): 0.5
Toxicity given I=1 (π_T|I=1): 0.55
Efficacy given I=0 (π_E|I=0): 0.481
Efficacy given I=1 (π_E|I=1): 0.583
Probability distributions:
P(T=0|I=0): 0.5 P(T=1|I=0): 0.5
P(T=0|I=1): 0.45 P(T=1|I=1): 0.55
P(E=0|I=0): 0.519 P(E=1|I=0): 0.481
P(E=0|I=1): 0.417 P(E=1|I=1): 0.583
Expected utility given I=0: 26.45
Expected utility given I=1: 40.96
Total expected utility: 35.42
Dose 5 Utility Calculation:
Immune response probability (π_I): 0.683
Toxicity given I=0 (π_T|I=0): 0.606
Toxicity given I=1 (π_T|I=1): 0.653
Efficacy given I=0 (π_E|I=0): 0.513
Efficacy given I=1 (π_E|I=1): 0.782
Probability distributions:
P(T=0|I=0): 0.394 P(T=1|I=0): 0.606
P(T=0|I=1): 0.347 P(T=1|I=1): 0.653
P(E=0|I=0): 0.487 P(E=1|I=0): 0.513
P(E=0|I=1): 0.218 P(E=1|I=1): 0.782
Expected utility given I=0: 25.49
Expected utility given I=1: 48.32
Total expected utility: 41.08
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.170 | 0.067 | 0.155 | 0.127 | 0.277 | 9.7 | 31.2 | 13.4
2 | 0.295 | 0.068 | 0.165 | 0.171 | 0.311 | 13.1 | 33.8 | 19.2
3 | 0.557 | 0.218 | 0.259 | 0.374 | 0.494 | 25.8 | 45.5 | 36.8
4 | 0.618 | 0.500 | 0.550 | 0.481 | 0.583 | 26.5 | 41.0 | 35.4
5 | 0.683 | 0.606 | 0.653 | 0.513 | 0.782 | 25.5 | 48.3 | 41.1
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0 0.3428895 0.6571105 0 0
--- Stage 4 ---
Workflow: Step 1 - Adaptive randomization (using probabilities from previous stage)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.071 0.083 0.191 0.524 0.632
Summary: Efficacy marginal means: 0.156 0.239 0.488 0.579 0.709
Summary: Immune response means: 0.173 0.306 0.58 0.628 0.694
Dose 1 : P(Tox < 0.35 ) = 1 (Threshold: 0.5 ) P(Eff > 0.1 ) = 0.74 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.39 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.35 ) = 1 (Threshold: 0.5 ) P(Eff > 0.1 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.9 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.35 ) = 0.98 (Threshold: 0.5 ) P(Eff > 0.1 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 1 (Threshold: 0.5 )
Dose 4 : P(Tox < 0.35 ) = 0.11 (Threshold: 0.5 ) P(Eff > 0.1 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 1 (Threshold: 0.5 )
Dose 5 : P(Tox < 0.35 ) = 0.02 (Threshold: 0.5 ) P(Eff > 0.1 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 1 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2 3
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.173
Toxicity given I=0 (π_T|I=0): 0.06
Toxicity given I=1 (π_T|I=1): 0.125
Efficacy given I=0 (π_E|I=0): 0.113
Efficacy given I=1 (π_E|I=1): 0.357
Probability distributions:
P(T=0|I=0): 0.94 P(T=1|I=0): 0.06
P(T=0|I=1): 0.875 P(T=1|I=1): 0.125
P(E=0|I=0): 0.887 P(E=1|I=0): 0.113
P(E=0|I=1): 0.643 P(E=1|I=1): 0.357
Expected utility given I=0: 8.73
Expected utility given I=1: 38.67
Total expected utility: 13.9
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.306
Toxicity given I=0 (π_T|I=0): 0.061
Toxicity given I=1 (π_T|I=1): 0.132
Efficacy given I=0 (π_E|I=0): 0.155
Efficacy given I=1 (π_E|I=1): 0.43
Probability distributions:
P(T=0|I=0): 0.939 P(T=1|I=0): 0.061
P(T=0|I=1): 0.868 P(T=1|I=1): 0.132
P(E=0|I=0): 0.845 P(E=1|I=0): 0.155
P(E=0|I=1): 0.57 P(E=1|I=1): 0.43
Expected utility given I=0: 11.89
Expected utility given I=1: 44.49
Total expected utility: 21.88
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.58
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.22
Efficacy given I=0 (π_E|I=0): 0.346
Efficacy given I=1 (π_E|I=1): 0.593
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.78 P(T=1|I=1): 0.22
P(E=0|I=0): 0.654 P(E=1|I=0): 0.346
P(E=0|I=1): 0.407 P(E=1|I=1): 0.593
Expected utility given I=0: 25.05
Expected utility given I=1: 54.65
Total expected utility: 42.2
Dose 4 Utility Calculation:
Immune response probability (π_I): 0.628
Toxicity given I=0 (π_T|I=0): 0.49
Toxicity given I=1 (π_T|I=1): 0.544
Efficacy given I=0 (π_E|I=0): 0.488
Efficacy given I=1 (π_E|I=1): 0.634
Probability distributions:
P(T=0|I=0): 0.51 P(T=1|I=0): 0.49
P(T=0|I=1): 0.456 P(T=1|I=1): 0.544
P(E=0|I=0): 0.512 P(E=1|I=0): 0.488
P(E=0|I=1): 0.366 P(E=1|I=1): 0.634
Expected utility given I=0: 27.08
Expected utility given I=1: 44.37
Total expected utility: 37.95
Dose 5 Utility Calculation:
Immune response probability (π_I): 0.694
Toxicity given I=0 (π_T|I=0): 0.598
Toxicity given I=1 (π_T|I=1): 0.646
Efficacy given I=0 (π_E|I=0): 0.521
Efficacy given I=1 (π_E|I=1): 0.793
Probability distributions:
P(T=0|I=0): 0.402 P(T=1|I=0): 0.598
P(T=0|I=1): 0.354 P(T=1|I=1): 0.646
P(E=0|I=0): 0.479 P(E=1|I=0): 0.521
P(E=0|I=1): 0.207 P(E=1|I=1): 0.793
Expected utility given I=0: 26.08
Expected utility given I=1: 49.26
Total expected utility: 42.17
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.173 | 0.060 | 0.125 | 0.113 | 0.357 | 8.7 | 38.7 | 13.9
2 | 0.306 | 0.061 | 0.132 | 0.155 | 0.430 | 11.9 | 44.5 | 21.9
3 | 0.580 | 0.151 | 0.220 | 0.346 | 0.593 | 25.1 | 54.6 | 42.2
4 | 0.628 | 0.490 | 0.544 | 0.488 | 0.634 | 27.1 | 44.4 | 37.9
5 | 0.694 | 0.598 | 0.646 | 0.521 | 0.793 | 26.1 | 49.3 | 42.2
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0 0.3414691 0.6585309 0 0
--- Stage 5 ---
Workflow: Step 1 - Adaptive randomization (using probabilities from previous stage)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.061 0.072 0.22 0.536 0.635
Summary: Efficacy marginal means: 0.152 0.254 0.498 0.593 0.712
Summary: Immune response means: 0.168 0.321 0.581 0.635 0.699
Dose 1 : P(Tox < 0.35 ) = 1 (Threshold: 0.5 ) P(Eff > 0.1 ) = 0.74 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.38 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.35 ) = 1 (Threshold: 0.5 ) P(Eff > 0.1 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.95 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.35 ) = 0.97 (Threshold: 0.5 ) P(Eff > 0.1 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 1 (Threshold: 0.5 )
Dose 4 : P(Tox < 0.35 ) = 0.09 (Threshold: 0.5 ) P(Eff > 0.1 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 1 (Threshold: 0.5 )
Dose 5 : P(Tox < 0.35 ) = 0.01 (Threshold: 0.5 ) P(Eff > 0.1 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 1 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2 3
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.168
Toxicity given I=0 (π_T|I=0): 0.05
Toxicity given I=1 (π_T|I=1): 0.113
Efficacy given I=0 (π_E|I=0): 0.104
Efficacy given I=1 (π_E|I=1): 0.396
Probability distributions:
P(T=0|I=0): 0.95 P(T=1|I=0): 0.05
P(T=0|I=1): 0.887 P(T=1|I=1): 0.113
P(E=0|I=0): 0.896 P(E=1|I=0): 0.104
P(E=0|I=1): 0.604 P(E=1|I=1): 0.396
Expected utility given I=0: 8.03
Expected utility given I=1: 42.29
Total expected utility: 13.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.321
Toxicity given I=0 (π_T|I=0): 0.051
Toxicity given I=1 (π_T|I=1): 0.118
Efficacy given I=0 (π_E|I=0): 0.134
Efficacy given I=1 (π_E|I=1): 0.508
Probability distributions:
P(T=0|I=0): 0.949 P(T=1|I=0): 0.051
P(T=0|I=1): 0.882 P(T=1|I=1): 0.118
P(E=0|I=0): 0.866 P(E=1|I=0): 0.134
P(E=0|I=1): 0.492 P(E=1|I=1): 0.508
Expected utility given I=0: 10.38
Expected utility given I=1: 51.52
Total expected utility: 23.6
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.581
Toxicity given I=0 (π_T|I=0): 0.181
Toxicity given I=1 (π_T|I=1): 0.248
Efficacy given I=0 (π_E|I=0): 0.332
Efficacy given I=1 (π_E|I=1): 0.617
Probability distributions:
P(T=0|I=0): 0.819 P(T=1|I=0): 0.181
P(T=0|I=1): 0.752 P(T=1|I=1): 0.248
P(E=0|I=0): 0.668 P(E=1|I=0): 0.332
P(E=0|I=1): 0.383 P(E=1|I=1): 0.617
Expected utility given I=0: 23.55
Expected utility given I=1: 55.43
Total expected utility: 42.06
Dose 4 Utility Calculation:
Immune response probability (π_I): 0.635
Toxicity given I=0 (π_T|I=0): 0.5
Toxicity given I=1 (π_T|I=1): 0.555
Efficacy given I=0 (π_E|I=0): 0.485
Efficacy given I=1 (π_E|I=1): 0.654
Probability distributions:
P(T=0|I=0): 0.5 P(T=1|I=0): 0.5
P(T=0|I=1): 0.445 P(T=1|I=1): 0.555
P(E=0|I=0): 0.515 P(E=1|I=0): 0.485
P(E=0|I=1): 0.346 P(E=1|I=1): 0.654
Expected utility given I=0: 26.69
Expected utility given I=1: 45.15
Total expected utility: 38.4
Dose 5 Utility Calculation:
Immune response probability (π_I): 0.699
Toxicity given I=0 (π_T|I=0): 0.601
Toxicity given I=1 (π_T|I=1): 0.65
Efficacy given I=0 (π_E|I=0): 0.518
Efficacy given I=1 (π_E|I=1): 0.795
Probability distributions:
P(T=0|I=0): 0.399 P(T=1|I=0): 0.601
P(T=0|I=1): 0.35 P(T=1|I=1): 0.65
P(E=0|I=0): 0.482 P(E=1|I=0): 0.518
P(E=0|I=1): 0.205 P(E=1|I=1): 0.795
Expected utility given I=0: 25.89
Expected utility given I=1: 49.21
Total expected utility: 42.2
=======
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
>>>>>>> origin/main
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
<<<<<<< HEAD
1 | 0.168 | 0.050 | 0.113 | 0.104 | 0.396 | 8.0 | 42.3 | 13.8
2 | 0.321 | 0.051 | 0.118 | 0.134 | 0.508 | 10.4 | 51.5 | 23.6
3 | 0.581 | 0.181 | 0.248 | 0.332 | 0.617 | 23.6 | 55.4 | 42.1
4 | 0.635 | 0.500 | 0.555 | 0.485 | 0.654 | 26.7 | 45.1 | 38.4
5 | 0.699 | 0.601 | 0.650 | 0.518 | 0.795 | 25.9 | 49.2 | 42.2
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
--- PoC THRESHOLD CHECK ---
Admissible doses: 2 3
Pairwise probabilities Pr(π_I1 < delta_poc * π_Ij | D_n): 0.703 0.986
c_poc threshold: 0.95
P_final (doses passing PoC): 3
PoC detected (length(P_final) > 0): TRUE
=======
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
>>>>>>> origin/main
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
<<<<<<< HEAD
Admissible doses A: 2 3
Utilities: 23.6 42.06
Pairwise probabilities Pr(π_I1 < delta*π_Ij): 0.703 0.986
c_poc threshold: 0.95
P_final (PoC-eligible doses): 3
PoC detected: TRUE
Selected dose: 3
Selected utility: 42.06
Selection reason: PoC detected (P_final non-empty)
--- END FINAL SELECTION ---
Results
This chunk prints the final optimal dose and displays the plots.
# Print final results
cat ("
--- Final Results ---
" )
if (results$ terminated_early) {
cat ("Trial terminated early at stage:" , results$ termination_stage, "
" )
cat ("Reason:" , results$ termination_reason, "
" )
cat ("No Optimal Dose selected
" )
} else {
cat ("Final OD:" , results$ final_od, "
" )
cat ("Final utility:" , round (results$ final_utility, 2 ), "
" )
cat ("PoC validated:" , results$ poc_validated, "
" )
cat ("PoC probability:" , round (results$ poc_probability, 3 ), "
" )
cat ("Selection reason:" , results$ selection_reason, "
" )
}
Final OD: 3
Final utility: 42.06
PoC validated: TRUE
PoC probability: 0.703
Selection reason: PoC detected (P_final non-empty)
# Plot final results and save them with modern styling
plot_posterior_summary (results$ posterior_summaries$ imm, title = "Immune Response vs Dose (PAVA Adjusted)" , file_path = "results/plots/immune_response_refactored.png" , style = "modern" )
plot_posterior_summary (results$ posterior_summaries$ tox, title = "Toxicity Rate by Dose and Immune Status" , group_col = "Y_I" , file_path = "results/plots/toxicity_refactored.png" , style = "modern" )
plot_posterior_summary (results$ posterior_summaries$ eff, title = "Efficacy Rate by Dose and Immune Status" , group_col = "Y_I" , file_path = "results/plots/efficacy_refactored.png" , style = "modern" )
# Create dose-response curves similar to reference code
cat (" \n === Creating Dose-Response Curves === \n " )
=== Creating Dose-Response Curves ===
# Extract true probabilities for dose-response curves
true_toxicity <- p_YT_given_I[,1 ] * (1 - p_YI) + p_YT_given_I[,2 ] * p_YI
true_efficacy <- p_YE_given_I[,1 ] * (1 - p_YI) + p_YE_given_I[,2 ] * p_YI
# Calculate true utilities for all dose levels using true probabilities
true_utility <- sapply (1 : length (trial_config$ dose_levels),
calculate_utility_from_true_probs,
p_YI = p_YI,
p_YT_given_I = p_YT_given_I,
p_YE_given_I = p_YE_given_I,
utility_table = utility_table)
# Create dose-response curves plot
dose_response_plot <- plot_dose_response_curves (
toxicity_data = true_toxicity,
efficacy_data = true_efficacy,
utility_data = true_utility,
title = "True Dose-Response Curves" ,
file_path = "results/plots/dose_response_curves.png"
)
print (dose_response_plot)
# Plot allocation probabilities over time with modern styling
p_alloc_time <- ggplot (results$ all_alloc_probs, aes (x = Stage, y = Prob, color = factor (Dose))) +
geom_line (linewidth = 1 ) +
geom_point (size = 3 ) +
labs (title = "Allocation Probabilities Over Time" ,
x = "Stage" , y = "Allocation Probability" ,
color = "Dose Level" ) +
scale_color_manual (values = c ("#999999" , "#E69F00" , "#56B4E9" , "#009E73" , "#CC79A7" )) +
theme_bw (base_size = 16 ) +
theme (panel.grid = element_blank (),
plot.title = element_text (hjust = 0.5 ),
axis.line = element_line (color = "black" ))
print (p_alloc_time)
# Visualize participant allocation with better formatting
# Count participants per dose level and stage
allocation_summary <- results$ all_data %>%
group_by (d, stage) %>%
summarise (n_participants = n (), .groups = 'drop' ) %>%
mutate (d = factor (d), stage = factor (stage, levels = 1 : 5 , labels = paste ("Stage" , 1 : 5 )))
# Plot 1: Allocation by dose level and stage with modern styling
p_alloc <- ggplot (allocation_summary, aes (x = d, y = n_participants, fill = stage)) +
geom_bar (stat = "identity" , position = "dodge" , width = 0.7 , color = "black" ) +
labs (title = "Participant Allocation by Dose Level and Stage" ,
x = "Dose Level" , y = "Number of Participants" ,
subtitle = paste ("Total participants:" , sum (allocation_summary$ n_participants))) +
scale_fill_manual (name = "Stage" , values = c ("#999999" , "#E69F00" , "#56B4E9" , "#009E73" , "#CC79A7" )) +
theme_bw (base_size = 16 ) +
theme (panel.grid = element_blank (),
plot.title = element_text (size = 14 , face = "bold" , hjust = 0.5 ),
axis.text = element_text (size = 12 ),
axis.title = element_text (size = 12 ),
axis.line = element_line (color = "black" ))
print (p_alloc)
# Plot 2: Cumulative allocation over stages
cumulative_summary <- allocation_summary %>%
group_by (d) %>%
mutate (cumulative_participants = cumsum (n_participants)) %>%
ungroup ()
p_cumulative <- ggplot (cumulative_summary, aes (x = stage, y = cumulative_participants, color = d, group = d)) +
geom_line (linewidth = 1.5 ) +
geom_point (size = 3 ) +
labs (title = "Cumulative Participant Allocation Over Stages" ,
x = "Stage" , y = "Cumulative Number of Participants" ,
color = "Dose Level" ,
subtitle = paste ("Final total participants:" , sum (allocation_summary$ n_participants))) +
scale_color_manual (values = c ("#999999" , "#E69F00" , "#56B4E9" , "#009E73" , "#CC79A7" )) +
theme_bw (base_size = 16 ) +
theme (panel.grid = element_blank (),
plot.title = element_text (size = 14 , face = "bold" , hjust = 0.5 ),
axis.text = element_text (size = 12 ),
axis.title = element_text (size = 12 ),
axis.line = element_line (color = "black" ))
print (p_cumulative)
# Print summary statistics
cat (" \n === ALLOCATION SUMMARY === \n " )
=== ALLOCATION SUMMARY ===
cat ("Total participants:" , sum (allocation_summary$ n_participants), " \n " )
cat ("Participants per stage: \n " )
stage_totals <- allocation_summary %>%
group_by (stage) %>%
summarise (total = sum (n_participants), .groups = 'drop' )
for (i in 1 : nrow (stage_totals)) {
cat (" Stage" , i, ":" , stage_totals$ total[i], "participants \n " )
}
Stage 1 : 15 participants
Stage 2 : 15 participants
Stage 3 : 15 participants
Stage 4 : 15 participants
Stage 5 : 15 participants
Method Comparison Analysis
This section creates comparison plots similar to the reference code, showing how different methods or parameter settings would perform.
# Create example data for method comparison (similar to reference code)
cat (" \n === Creating Method Comparison Plots === \n " )
=== Creating Method Comparison Plots ===
# Simulate different method performances
methods <- c ("Current" , "Proposed" , "Reference" )
scenarios <- c ("Scenario 1" , "Scenario 2" , "Scenario 3" )
# OBD Selection Rate Comparison
obd_data <- expand.grid (
scenario = scenarios,
method = methods,
stringsAsFactors = FALSE
)
obd_data$ obd_rate <- c (45 , 60 , 55 , 70 , 65 , 50 , 80 , 85 , 75 )
# Create OBD selection plot
p_obd <- plot_method_comparison_bars (
obd_data,
x_var = "scenario" , y_var = "obd_rate" , fill_var = "method" ,
title = "OBD Selection Rate Comparison" ,
y_label = "OBD Selection (%)" ,
limits = c (0 , 100 ),
file_path = "results/plots/obd_selection_comparison.png"
)
Warning: `aes_string()` was deprecated in ggplot2 3.0.0.
ℹ Please use tidy evaluation idioms with `aes()`.
ℹ See also `vignette("ggplot2-in-packages")` for more information.
# Sample Size Comparison
sample_data <- expand.grid (
scenario = scenarios,
method = methods,
stringsAsFactors = FALSE
)
sample_data$ avg_n <- c (25 , 20 , 30 , 22 , 18 , 28 , 18 , 15 , 25 )
# Create sample size plot
p_sample <- plot_method_comparison_bars (
sample_data,
x_var = "scenario" , y_var = "avg_n" , fill_var = "method" ,
title = "Average Sample Size Comparison" ,
y_label = "Average Sample Size" ,
limits = c (0 , 35 ),
file_path = "results/plots/sample_size_comparison.png"
)
print (p_sample)
# Safety (Overdose) Comparison
safety_data <- expand.grid (
scenario = scenarios,
method = methods,
stringsAsFactors = FALSE
)
safety_data$ overdose_pct <- c (15 , 10 , 20 , 12 , 8 , 18 , 8 , 5 , 15 )
# Create safety plot
p_safety <- plot_method_comparison_bars (
safety_data,
x_var = "scenario" , y_var = "overdose_pct" , fill_var = "method" ,
title = "Overdose Patient Percentage" ,
y_label = "Overdose Pts (%)" ,
limits = c (0 , 25 ),
file_path = "results/plots/safety_comparison.png"
)
print (p_safety)
cat ("✅ Method comparison plots created successfully! \n " )
✅ Method comparison plots created successfully!
cat ("📁 All plots saved to results/plots/ directory \n " )
📁 All plots saved to results/plots/ directory
Multi-Scenario Analysis
This section creates multi-scenario dose-response curves similar to the reference code.
# Create multi-scenario analysis
cat (" \n === Creating Multi-Scenario Analysis === \n " )
=== Creating Multi-Scenario Analysis ===
# Define different scenarios with varying parameters
scenarios_data <- list (
list (
toxicity = c (0.1 , 0.18 , 0.35 , 0.40 , 0.50 ),
efficacy = c (0.35 , 0.35 , 0.37 , 0.39 , 0.39 ),
utility = c (0.27 , 0.23 , 0.10 , 0.13 , 0.17 )
),
list (
toxicity = c (0.05 , 0.15 , 0.25 , 0.35 , 0.50 ),
efficacy = c (0.10 , 0.35 , 0.35 , 0.38 , 0.39 ),
utility = c (0.07 , 0.22 , 0.22 , 0.12 , 0.06 )
),
list (
toxicity = c (0.02 , 0.06 , 0.10 , 0.20 , 0.35 ),
efficacy = c (0.05 , 0.10 , 0.35 , 0.35 , 0.40 ),
utility = c (0.03 , 0.07 , 0.28 , 0.22 , 0.13 )
)
)
# Create multi-scenario plot
multi_scenario_plot <- plot_multi_scenario_curves (
scenarios_data,
title = "Dose-Response Curves Across Scenarios" ,
file_path = "results/plots/multi_scenario_analysis.png"
)
Scale for y is already present.
Adding another scale for y, which will replace the existing scale.
print (multi_scenario_plot)
cat ("✅ Multi-scenario analysis completed! \n " )
✅ Multi-scenario analysis completed!
=======
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.7
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
PoC detection rate = 0.000 (95% CI: [0.000, 0.036])
Progress: 2/6 - Testing C_poc = 0.750
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.75
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
PoC detection rate = 0.000 (95% CI: [0.000, 0.036])
Progress: 3/6 - Testing C_poc = 0.800
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.8
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
PoC detection rate = 0.000 (95% CI: [0.000, 0.036])
Progress: 4/6 - Testing C_poc = 0.850
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.85
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
PoC detection rate = 0.000 (95% CI: [0.000, 0.036])
Progress: 5/6 - Testing C_poc = 0.900
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.9
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
PoC detection rate = 0.000 (95% CI: [0.000, 0.036])
Progress: 6/6 - Testing C_poc = 0.950
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
--- Stage 1 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.235 0.322 0.428
Summary: Efficacy marginal means: 0.556 0.629 0.664
Summary: Immune response means: 0.285 0.305 0.357
Dose 1 : P(Tox < 0.3 ) = 0.73 (Threshold: 0.5 ) P(Eff > 0.2 ) = 0.99 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.76 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.45 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.8 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.18 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.87 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.285
Toxicity given I=0 (π_T|I=0): 0.194
Toxicity given I=1 (π_T|I=1): 0.335
Efficacy given I=0 (π_E|I=0): 0.531
Efficacy given I=1 (π_E|I=1): 0.62
Probability distributions:
P(T=0|I=0): 0.806 P(T=1|I=0): 0.194
P(T=0|I=1): 0.665 P(T=1|I=1): 0.335
P(E=0|I=0): 0.469 P(E=1|I=0): 0.531
P(E=0|I=1): 0.38 P(E=1|I=1): 0.62
Expected utility given I=0: 37.35
Expected utility given I=1: 52.03
Total expected utility: 41.54
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.305
Toxicity given I=0 (π_T|I=0): 0.247
Toxicity given I=1 (π_T|I=1): 0.496
Efficacy given I=0 (π_E|I=0): 0.615
Efficacy given I=1 (π_E|I=1): 0.662
Probability distributions:
P(T=0|I=0): 0.753 P(T=1|I=0): 0.247
P(T=0|I=1): 0.504 P(T=1|I=1): 0.496
P(E=0|I=0): 0.385 P(E=1|I=0): 0.615
P(E=0|I=1): 0.338 P(E=1|I=1): 0.662
Expected utility given I=0: 41.58
Expected utility given I=1: 48.22
Total expected utility: 43.61
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.357
Toxicity given I=0 (π_T|I=0): 0.32
Toxicity given I=1 (π_T|I=1): 0.626
Efficacy given I=0 (π_E|I=0): 0.634
Efficacy given I=1 (π_E|I=1): 0.717
Probability distributions:
P(T=0|I=0): 0.68 P(T=1|I=0): 0.32
P(T=0|I=1): 0.374 P(T=1|I=1): 0.626
P(E=0|I=0): 0.366 P(E=1|I=0): 0.634
P(E=0|I=1): 0.283 P(E=1|I=1): 0.717
Expected utility given I=0: 40.58
Expected utility given I=1: 45.83
Total expected utility: 42.46
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.285 | 0.194 | 0.335 | 0.531 | 0.620 | 37.4 | 52.0 | 41.5
2 | 0.305 | 0.247 | 0.496 | 0.615 | 0.662 | 41.6 | 48.2 | 43.6
3 | 0.357 | 0.320 | 0.626 | 0.634 | 0.717 | 40.6 | 45.8 | 42.5
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 1 0 0
--- Stage 2 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.143 0.291 0.416
Summary: Efficacy marginal means: 0.644 0.675 0.699
Summary: Immune response means: 0.237 0.276 0.344
Dose 1 : P(Tox < 0.3 ) = 0.95 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.63 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.57 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.73 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.22 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.86 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 1 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.237
Toxicity given I=0 (π_T|I=0): 0.109
Toxicity given I=1 (π_T|I=1): 0.255
Efficacy given I=0 (π_E|I=0): 0.632
Efficacy given I=1 (π_E|I=1): 0.688
Probability distributions:
P(T=0|I=0): 0.891 P(T=1|I=0): 0.109
P(T=0|I=1): 0.745 P(T=1|I=1): 0.255
P(E=0|I=0): 0.368 P(E=1|I=0): 0.632
P(E=0|I=1): 0.312 P(E=1|I=1): 0.688
Expected utility given I=0: 47.08
Expected utility given I=1: 60.58
Total expected utility: 50.27
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.276
Toxicity given I=0 (π_T|I=0): 0.218
Toxicity given I=1 (π_T|I=1): 0.483
Efficacy given I=0 (π_E|I=0): 0.663
Efficacy given I=1 (π_E|I=1): 0.706
Probability distributions:
P(T=0|I=0): 0.782 P(T=1|I=0): 0.218
P(T=0|I=1): 0.517 P(T=1|I=1): 0.483
P(E=0|I=0): 0.337 P(E=1|I=0): 0.663
P(E=0|I=1): 0.294 P(E=1|I=1): 0.706
Expected utility given I=0: 45.79
Expected utility given I=1: 51.67
Total expected utility: 47.42
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.344
Toxicity given I=0 (π_T|I=0): 0.309
Toxicity given I=1 (π_T|I=1): 0.62
Efficacy given I=0 (π_E|I=0): 0.676
Efficacy given I=1 (π_E|I=1): 0.744
Probability distributions:
P(T=0|I=0): 0.691 P(T=1|I=0): 0.309
P(T=0|I=1): 0.38 P(T=1|I=1): 0.62
P(E=0|I=0): 0.324 P(E=1|I=0): 0.676
P(E=0|I=1): 0.256 P(E=1|I=1): 0.744
Expected utility given I=0: 43.64
Expected utility given I=1: 47.71
Total expected utility: 45.04
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.237 | 0.109 | 0.255 | 0.632 | 0.688 | 47.1 | 60.6 | 50.3
2 | 0.276 | 0.218 | 0.483 | 0.663 | 0.706 | 45.8 | 51.7 | 47.4
3 | 0.344 | 0.309 | 0.620 | 0.676 | 0.744 | 43.6 | 47.7 | 45.0
--- End Utility Calculations ---
Workflow: Step 3 - Adaptive Randomization (allocate patients based on utility scores)
Allocation probabilities for next stage: 0.5146174 0.4853826 0
--- Stage 3 ---
Workflow: Step 1 - Equal randomization (Stage 1) or Adaptive randomization (Stages 2+)
Workflow: Step 2 - Interim Analysis (update admissible set based on posterior probabilities)
--- Admissibility Check ---
Summary: Toxicity marginal means: 0.109 0.22 0.391
Summary: Efficacy marginal means: 0.694 0.709 0.725
Summary: Immune response means: 0.204 0.219 0.316
Dose 1 : P(Tox < 0.3 ) = 0.99 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.48 (Threshold: 0.5 )
Dose 2 : P(Tox < 0.3 ) = 0.8 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.53 (Threshold: 0.5 )
Dose 3 : P(Tox < 0.3 ) = 0.29 (Threshold: 0.5 ) P(Eff > 0.2 ) = 1 (Threshold: 0.5 ) P(Imm > 0.2 ) = 0.77 (Threshold: 0.5 )
--- End Admissibility Check ---
Admissible set: 2
Workflow: Step 4 - Early Termination Check
--- Utility Score Calculations ---
Utility Table Reference:
I=0 (No Immune Response):
E=0, T=0: 0 E=1, T=0: 80
E=0, T=1: 0 E=1, T=1: 30
I=1 (Immune Response):
E=0, T=0: 10 E=1, T=0: 100
E=0, T=1: 0 E=1, T=1: 40
Dose 1 Utility Calculation:
Immune response probability (π_I): 0.204
Toxicity given I=0 (π_T|I=0): 0.083
Toxicity given I=1 (π_T|I=1): 0.207
Efficacy given I=0 (π_E|I=0): 0.684
Efficacy given I=1 (π_E|I=1): 0.733
Probability distributions:
P(T=0|I=0): 0.917 P(T=1|I=0): 0.083
P(T=0|I=1): 0.793 P(T=1|I=1): 0.207
P(E=0|I=0): 0.316 P(E=1|I=0): 0.684
P(E=0|I=1): 0.267 P(E=1|I=1): 0.733
Expected utility given I=0: 51.84
Expected utility given I=1: 66.29
Total expected utility: 54.79
Dose 2 Utility Calculation:
Immune response probability (π_I): 0.219
Toxicity given I=0 (π_T|I=0): 0.151
Toxicity given I=1 (π_T|I=1): 0.469
Efficacy given I=0 (π_E|I=0): 0.699
Efficacy given I=1 (π_E|I=1): 0.741
Probability distributions:
P(T=0|I=0): 0.849 P(T=1|I=0): 0.151
P(T=0|I=1): 0.531 P(T=1|I=1): 0.469
P(E=0|I=0): 0.301 P(E=1|I=0): 0.699
P(E=0|I=1): 0.259 P(E=1|I=1): 0.741
Expected utility given I=0: 50.63
Expected utility given I=1: 54.65
Total expected utility: 51.51
Dose 3 Utility Calculation:
Immune response probability (π_I): 0.316
Toxicity given I=0 (π_T|I=0): 0.287
Toxicity given I=1 (π_T|I=1): 0.609
Efficacy given I=0 (π_E|I=0): 0.706
Efficacy given I=1 (π_E|I=1): 0.768
Probability distributions:
P(T=0|I=0): 0.713 P(T=1|I=0): 0.287
P(T=0|I=1): 0.391 P(T=1|I=1): 0.609
P(E=0|I=0): 0.294 P(E=1|I=0): 0.706
P(E=0|I=1): 0.232 P(E=1|I=1): 0.768
Expected utility given I=0: 46.36
Expected utility given I=1: 49.63
Total expected utility: 47.4
Utility Summary Table:
Dose | Immune | Tox(I=0) | Tox(I=1) | Eff(I=0) | Eff(I=1) | U(I=0) | U(I=1) | Total U
-----|--------|----------|----------|----------|----------|--------|--------|--------
1 | 0.204 | 0.083 | 0.207 | 0.684 | 0.733 | 51.8 | 66.3 | 54.8
2 | 0.219 | 0.151 | 0.469 | 0.699 | 0.741 | 50.6 | 54.7 | 51.5
3 | 0.316 | 0.287 | 0.609 | 0.706 | 0.768 | 46.4 | 49.6 | 47.4
--- End Utility Calculations ---
Workflow: Step 5 - Final Selection with PoC validation
PoC calculation for dose 2: Πᵢ=0.669±0.148, Πᵢⱼ=0.669±0.148, PoC=0.000
--- PoC THRESHOLD CHECK ---
Maximum PoC probability: 0
PoC threshold: 0.95
PoC threshold met: FALSE
--- END PoC CHECK ---
--- FINAL DOSE SELECTION WITH PoC ---
Admissible doses: 2
Utilities: 51.51
Selected dose: 2
Selected utility: 51.51
PoC validated: FALSE
Max PoC probability: 0
Selection reason: PoC threshold not met, but selecting best available dose
--- END FINAL SELECTION ---
PoC detection rate = 0.000 (95% CI: [0.000, 0.036])
=== CALIBRATION COMPLETE ===
Optimal C_poc = 0.700
Achieved detection rate = 0.000 (target: 0.100)
Difference from target = 0.100
============================